# Damped Motion In Exercises 11-14, consider a damped mass-spring system whose motion is described by the differential equation d 2 y d t 2 + 2 λ d y d t + ω 2 y = 0 The zeros of its characteristic equation are m 1 = − λ + λ 2 − ω 2 and m 1 = − λ − λ 2 − ω 2 For λ 2 − ω 2 &gt; 0 , the system is overdamped; λ 2 − ω 2 = 0 , it is critically damped; and for λ 2 − ω 2 &lt; 0 , it is underdamped. Determine whether the differential equation represents an overdamped, critically damped, or underdamped system. Find the particular solution that satisfies the initial conditions. Use a graphing utility to graph the particular solution found in part (b). Explain how the graph illustrates the type of damping in the system. d 2 y d t 2 + 8 d y d t + 16 y = 0 y ( 0 ) = 1 and y ′ ( 0 ) = 1

### Multivariable Calculus

11th Edition
Ron Larson + 1 other
Publisher: Cengage Learning
ISBN: 9781337275378

### Multivariable Calculus

11th Edition
Ron Larson + 1 other
Publisher: Cengage Learning
ISBN: 9781337275378

#### Solutions

Chapter 16, Problem 11PS
Textbook Problem

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